For any , there exists a such that the sequence
See also Dirichlet's Theorem, Fermat 4n+1 Theorem, Sierpinski's Composite Number Theorem
References
Abel, U. and Siebert, H. ``Sequences with Large Numbers of Prime Values.'' Amer. Math. Monthly 100, 167-169, 1993.
Ageev, A. A. ``Sierpinski's Theorem is Deducible from Euler and Dirichlet.'' Amer. Math. Monthly 101, 659-660, 1994.
Forman, R. ``Sequences with Many Primes.'' Amer. Math. Monthly 99, 548-557, 1992.
Garrison, B. ``Polynomials with Large Numbers of Prime Values.'' Amer. Math. Monthly 97, 316-317, 1990.
Sierpinski, W. ``Les binômes et les nombres premiers.'' Bull. Soc. Roy. Sci. Liege 33, 259-260, 1964.